Finding mixed-strategy equilibria of continuous-action games without gradients using randomized policy networks

We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. Such game access is common in reinforcement learning settings, where the environment is typically treated as a black box. To tackle this problem, we apply zeroth-order optimization techniques that combine smoothed gradient estimators with equilibrium-finding dynamics. We model players' strategies using artificial neural networks. In particular, we use randomized policy networks to model mixed strategies. These take noise in addition to an observation as input and can flexibly represent arbitrary observation-dependent, continuous-action distributions. Being able to model such mixed strategies is crucial for tackling continuous-action games that lack pure-strategy equilibria. We evaluate the performance of our method using an approximation of the Nash convergence metric from game theory, which measures how much players can benefit from unilaterally changing their strategy. We apply our method to continuous Colonel Blotto games, single-item and multi-item auctions, and a visibility game. The experiments show that our method can quickly find high-quality approximate equilibria. Furthermore, they show that the dimensionality of the input noise is crucial for performance. To our knowledge, this paper is the first to solve general continuous-action games with unrestricted mixed strategies and without any gradient information

Machine learning applied to the context of Poker

A combinação de princípios da teoria de jogo e metodologias de machine learning aplicados ao contexto de formular estratégias ótimas para jogos está a angariar interesse por parte de uma porção crescentemente significativa da comunidade científica, tornando-se o jogo do Poker num candidato de estudo popular devido à sua natureza de informação imperfeita. Avanços nesta área possuem vastas aplicações em cenários do mundo real, e a área de investigação de inteligência artificial demonstra que o interesse relativo a este objeto de estudo está longe de desaparecer, com investigadores do Facebook e Carnegie Mellon a apresentar, em 2019, o primeiro agente de jogo autónomo de Poker provado como ganhador num cenário com múltiplos jogadores, uma conquista relativamente à anterior especificação do estado da arte, que fora desenvolvida para jogos de apenas 2 jogadores. Este estudo pretende explorar as características de jogos estocásticos de informação imperfeita, recolhendo informação acerca dos avanços nas metodologias disponibilizados por parte de investigadores de forma a desenvolver um agente autónomo de jogo que se pretende inserir na classificação de "utility-maximizing decision-maker".The combination of game theory principles and machine learning methodologies applied to encountering optimal strategies for games is garnering interest from an increasing large portion of the scientific community, with the game of Poker being a popular study subject due to its imperfect information nature. Advancements in this area have a wide array of applications in real-world scenarios, and the field of artificial intelligent studies show that the interest regarding this object of study is yet to fade, with researchers from Facebook and Carnegie Mellon presenting, in 2019, the world’s first autonomous Poker playing agent that is proven to be profitable while confronting multiple players at a time, an achievement in relation to the previous state of the art specification, which was developed for two player games only. This study intends to explore the characteristics of stochastic games of imperfect information, gathering information regarding the advancements in methodologies made available by researchers in order to ultimately develop an autonomous agent intended to adhere to the classification of a utility-maximizing decision-maker

Competition and well-being: does market competition make people unhappy?

Empirical research on the role of economic institutions for subjective well-being is still widely lacking, while recent economic-experimental outcomes suggest that experienced utility may depend on the intensity of market competition. This paper is the first to empirically analyze the implication of market competition for subjective well-being using real-life survey data on 80,000 individuals in more than 60 countries from the World Values Survey 1997-2001. In support of our hypothesis, we find that market competition aggravates the impact of individual’s bargaining position in economic transactions on her subjective well-being – compared to the least powerful in society. Put differently, we find that market competition enlarges the happiness differences caused by cleavages in socio-economic position. Our results also suggest that competition induced welfare changes are not gender-specific, while a stronger rule of law appears to prevent the generation of such additional benefits or losses. Particularly the latter results call for further economic-experimental corroboration in the laboratory, but also bear important policy implications.Subjective well-being; happiness; utility; competition; rule of law; completeness of contract; laboratory experiment; World Values Survey